** Archivi** J. Phys. A (2007)

** Author** Vieri Mastropietro

** Title ***Absence of logarithmic divergences
in the spin and charge density correlations of the $1d$ Hubbard model *

** Abstract **
We perform a rigorous computation
of the spin and charge density correlations of the 1d repulsive
Hubbard model at weak coupling, focusing on the properties of the Fourier
transform at momentum 0 and 2 p_F,
if $p_F$ is the Fermi momentum.
We prove that the interaction changes the
singularity at 2 p_F (the discontinuity
in the derivative becomes a power
law singularity) while the singularity at 0
is essentially unchanged. Our results show that the logarithmic divergences
at zero momentum recently found in a recent ppaer by Ferraz et al.,
which would be in contrast with Luttinger liquid behaviour, are indeed spurious.

** Keywords ** Hubbard model, response functions, Ward Identities

Vieri Mastropietro
Last modified: Sat Feb 18 14:42:23 CET 2007